Problem: Umaima is 3 times as old as Christopher. Twelve years ago, Umaima was 5 times as old as Christopher. How old is Christopher now?
Solution: We can use the given information to write down two equations that describe the ages of Umaima and Christopher. Let Umaima's current age be $u$ and Christopher's current age be $c$ The information in the first sentence can be expressed in the following equation: $u = 3c$ Twelve years ago, Umaima was $u - 12$ years old, and Christopher was $c - 12$ years old. The information in the second sentence can be expressed in the following equation: $u - 12 = 5(c - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $c$ , it might be easiest to use our first equation for $u$ and substitute it into our second equation. Our first equation is: $u = 3c$ . Substituting this into our second equation, we get: $3c$ $-$ $12 = 5(c - 12)$ which combines the information about $c$ from both of our original equations. Simplifying the right side of this equation, we get: $3 c - 12 = 5 c - 60$ Solving for $c$ , we get: $2 c = 48.$ $c = 24$.